B1 P&C Insurance Company Valuation
R. Goldfarb
April 10, 2016
Cliff’s Summary
Know how to get the discount rate and growth rate for each of the 3 method
DDM:
\(V_0 = \dfrac{\mathrm{E}[Div_1]}{k - g}\)
Knows how this can transform to the P:E formula
Remembers the terminal value formula uses CF at 1 but get you to time 0
FCFE:
\(FCFE = NI + (Non \:Cash\:Charges) - \Delta Working \:Capital - \Delta Capital + \Delta Debt\)
Discount all the FCFE for \(V_0\)
AE:
\(\begin{align} V_0 = BV_0 + \sum_{t=1} \frac{\overbrace{(ROE_t - k)BV_{t-1}}^{AE_t}}{(1+k)^t}\end{align}\)
Remember to add the \(BV_0\)
Relative multiples:
\(\dfrac{P_0}{E_1} = \dfrac{1 - \rho}{k - \rho \times ROE}\); Based on DDM
\(\dfrac{P_0}{BV_0} = 1 + \dfrac{ROE - k}{k - g}\); Based on AE
Types of Exam Questions
Haven’t done TIA practice questions
Concepts
- \(\star\) 2011 - #12 a: higher \(g\) should be matched with higher \(\beta\) for being more risky
- 2011 - #12 c: relationship between \(g\) and \(k\)
- 2015 #17 b-c: \(\beta\) discussion
DDM
- 2008 #43: DDM calc and convert to P:E
- \(\star\) 2008 #44: DDM calc and interpretation
- 2008 #45: Comparison on P:E
- 2009 #34
- 2011 - #12 b: DDM calc (Get \(r_f\) as t-bond less liquidity premium)
- \(\star\) 2012 #12: Full calc with DDM
- 2014 #16: DDM calc
- 2015 #17 a: DDM calc
FCFE
- \(\star\) 2009 #35: Full FCFE calc
- \(\star\) 2013 #11: Full FCFE calc with discussion
- 2014 #17: FCFE Calc; Not sure bout the reserve increase impact on required capital
- \(\star\) 2015 #16: Discussion on DCF
AE
- \(\star\) 2010 #31: Full AE calc
- 2011 - #13: Price to Book value calc + discussion on assumption
- 2013 #12: Full AE Calc + discussion
- 2015 #15: AE Calc + discussion
Relative Valuation
- \(\star\) 2014 #15: Price to Book calc using all the ratios given by LoB
Assumptions
Key assumptions are cost of captial \(k\) and growth rate \(g\)
Risk Adjusted Discount Rate
Recognize the risky cashflow by discounting them at a rate higher than the risk-free rate based on CAPM
\(k = r_f + \beta \left [ \mathrm{E}(r_m) - r_f \right ]\)
Risk of an investment depends on the rest of an investor’s portfolio. We focus instead on equilibrium rates of return
Different BU has different risk profile \(\Rightarrow\) Different discount rates
Discount rates can vary by period if business mix change
Not all cash flow have the same risk profile (premium, investment income, paid losses)
Simplification is to use average discount rate for the portfolio
One alternative way to account for the risky cash flow is to convert the cash flow to certainty equivalent cash flows and discount with risk free instead of the cost of capital
- Reflect the risk in the cashflow directly
Risk free Rate: \(r_f\)
- 90 days t-bill
- Maturity matched t-notes
- T-bonds less liquidity & term premium (~1.2%)
Market Risk Premium: \(\mathrm{E}(r_m) - r_f\)
6-8% historically
\(r_f\) here should be consistent
Need to sensitivity test
Systematic Market Risk: \(\beta\)
Based on regression on stock return vs market return
Can use industry \(\beta\)
Mix of business needs to be similar to industry
Industry \(\beta\) should be adjusted for differences in the industry leverage and company leverage
\(\beta\) will be higher for firms with more leverage, riskier business units
Alternative is to use all equity \(\beta\) to remove bias from leverage
Higher growth should have higher \(\beta\)
Insurance company has additional leverage from policyholder liabilities
Can assume total leverage of insurance companies is similar
Growth Rate
Used for the period after the forecast horizon
| Method | Growth Rate: \(g\) |
|---|---|
| DDM | \(ROE \times \rho\) |
| FCFE | \(ROE \times\) [Reinvestment Rate] |
| AE | At most the growth in book value |
Return on Equity: \(ROE\)
\(\dfrac{NI}{BE} = \dfrac{\text{Net Income after Tax}}{\text{Beginning Equity}}\)
Plowback Ratio: \(\rho\)
% of \(NI\) that is reinvested in the firm
- Company that have high growth should retain more earnings
Reinvestment Rate
\(\dfrac{\Delta Capital}{NI}\)
Dividend Discount Model (DDM)
\(V_0 = \dfrac{\mathrm{E}[Div_1]}{k - g}\)
\(Div_1\) is paid at the end of year 1
Constant growth assumption
\(\mathrm{E}[Div_1] = (1 - \rho) NI\)
Typically forecast a few years and use the above formula for the terminal value
Need to use \(NI\) after tax
When calculating \(g\), calculate \(ROE\) and \(g\) for all years and make selection
Firm with high expected growth tend to be riskier \(\Rightarrow\) Higher discount rate
- Forecast is more susceptible to being wrong, so should be discount more?
DDM Assumptions
- Expected dividends
- Dividend growth rate
- Risk-adjusted discount rate (From CAPM)
Free Cash Flow to Equity (FCFE)
Free cash flow available to pay shareholders:
\(FCFE = NI + (Non \:Cash\:Charges) - \Delta Working \:Capital - \Delta Capital + \Delta Debt\) Memorize Formula
\(\Delta\) loss reserve reflected in \(NI\) only; it gets netted out as non-cash charges and capital expenditures
\(NI\) is net of interest payments to shareholders, after tax
\(g = ROE \times\) [Reinvestment Rate] \(= ROE \times \dfrac{\Delta Capital}{NI}\)
- Assume portion of FCF not paid out is invested at \(k\)
Free Cash Flow
Cash flow available to pay out to the firm’s source of capital (for FCFE this is only to equity) net of amounts required to be reinvested to the firm for growth
Weakness: require forecasting financial statements, use adjusted accounting measure, large terminal value
Similar to DDM, calculate the \(ROE\) and reinvestment rate for all years and make a pick
- We don’t use the free cash flow to firm because there’s additional leverage for p/h liabilities from reserves held
- Not clear how to calculate cost of capital due to leverage from 2 different source and it complicates the calculation
- Using FCFE removes the source of leverage
- Dividend are discretionary
- Firms also return funds via stock buybacks
- Focus on free cash flow
Abnormal Earnings (AE)
Works with accounting measures of income
Need to remove distortions
More accurate some say
Clean surplus assumption
Requires all changes to book value (on the b/s) flow through the I/S
Flow through as earnings, dividends or capital contributions
\(V_0 = BV_0 + \begin{align}\sum_{t=1} \frac{AE_t}{(1+k)^t}\end{align}\)
\(AE_t = NI_t - k \cdot BV_{t-1} = (ROE_t - k)BV_{t-1}\) Important Formula
Earnings (net income) XS of cost of capital
Assume AE will trend to zero overtime since it’s difficult to maintain
AE is difficult to maintain as competitors will see the AE and move into the market
\(BV_0\)
Reported book value
Focus on tangible book value (e.g. take out goodwill)
Remove any systematic bias such as over or understated reserve
\(NI\) is net of interest payments to shareholders, after tax; Same as DCF model
Make complement of the book value adjustments here
e.g. any direct adjustment to the B/S that doesn’t flow from the I/S you have to adjust hereIf reserve is discounted in the \(BV_0\), need to change (lower) the \(ROE\) as the income will be generated from a larger capital base
\(g\)
Should be negative as AE tend to 0
Does not require additional capital as the growth from that extra capital will not accrue to today’s shareholders
Focus on value creation
Earnings above the required return on capital
Dividends and CF are just consequence of value creation
Small terminal value as it focus on any added value so less leverage
Directly using accounting measures so does not need to adjust into a cash flow measure
Relative Multiples
We don’t compare to sales because of leverage from p/h’s liability
Stock price can fluctuate so use an average price
Multiples can vary significantly even over short periods of time
Assumptions
Constant \(ROE\), \(\rho\), and \(k\)
Price to Earnings
Based on DDM
\(\dfrac{P_0}{E_1} = \dfrac{1 - \rho}{k - \underbrace{\rho \times ROE}_{g}}\) Memorize Formula
- If \(ROE > k\) \(\Rightarrow\) Keep a high \(\rho\)
P:E Ratio
Forward or leading P/E = consensus forecast earnings for next year
Trailing P/E = last year’s actual; Can be distorted by unusual events
Price = value of the firm derived from any of the methods
Earnings = \(NI\); Either forward or trailing
By default, apply the ratio to next year’s earnings per formula
Alternative use of P/E
Validating assumptions: reasonability check on the forecast
Shortcut to valuation: if you think company will grow similar to the industry
Terminal value: use the other method for the forecast horizon then P/E for the terminal value
Price to Book
Based on AE method
\(\dfrac{P_0}{BV_0} = 1 + \dfrac{ROE - k}{k - g}\) Memorize Formula
\(BV_0 =\) equity @ t = 0
Useful for firms with substantial holdings in marketable securities
Transaction Multiples
Can use multiples from transaction, however caveat:
Companies tend to overpay
- Control premium, and other reason M&A overpay
IPO’s are under priced
Financials used to value the transaction could be different from the information being used now (forecast is different)
Economic conditions @ transaction \(\neq\) economic conditions now
Relative Valuation for Multi-line firms
Use multiples from pure play peers (monoline firms) to estimate by division
Or compare multiples from diversified insurers
- Choose firms with similar business, \(ROE\), claims paying rating, \(\beta\)
